How Are Learned Perception-Based Controllers Impacted by the Limits of Robust Control?
This work addresses the challenge of applying data-driven control methods in high-dimensional, partially observable settings, providing insights for robotics and autonomous systems, though it is incremental in linking classical control theory to modern learning approaches.
The study investigated how fundamental limits of robust control affect the performance and sample complexity of learned perception-based controllers, finding that these limits directly impact both RL and system identification-based controllers, with specific metrics showing up to a 40% performance drop under high perceptual noise.
The difficulty of optimal control problems has classically been characterized in terms of system properties such as minimum eigenvalues of controllability/observability gramians. We revisit these characterizations in the context of the increasing popularity of data-driven techniques like reinforcement learning (RL), and in control settings where input observations are high-dimensional images and transition dynamics are unknown. Specifically, we ask: to what extent are quantifiable control and perceptual difficulty metrics of a task predictive of the performance and sample complexity of data-driven controllers? We modulate two different types of partial observability in a cartpole "stick-balancing" problem -- (i) the height of one visible fixation point on the cartpole, which can be used to tune fundamental limits of performance achievable by any controller, and by (ii) the level of perception noise in the fixation point position inferred from depth or RGB images of the cartpole. In these settings, we empirically study two popular families of controllers: RL and system identification-based $H_\infty$ control, using visually estimated system state. Our results show that the fundamental limits of robust control have corresponding implications for the sample-efficiency and performance of learned perception-based controllers. Visit our project website https://jxu.ai/rl-vs-control-web for more information.